Question

I wish to test whether Are X₄, X₅, and X₆ jointly significant for explaining Y and run two regressions using a sample of 30 observations.

1) Y= β₁ + β₂X₂ + β₃X₃ + β₄X₄ + β₅X₅ + β₆X₆ + u R² = .60 and TSS = 800

2) Y = β₁ + β₂X₂ + β₃X₃ + u R² = 0.3945 and TSS = 700

Test whether X₄, X₅, and X₆ jointly significant for explaining Y.

• A. None of these answers are correct.

• B.

  Yes, at least one of these explanatory variables are important for explaining variation in Y because the R-squared has increased.

• C.

  The test statistic is 2.60, and we conclude that none of these explanatory variables are statistically associated with variation in Y.

• D.

  The test statistic is 1.96, and we conclude that at least one of these variables X₄, X₅, and X₆ is important for explaining variation in Y.

• E.

  The test statistic is 2.60, and we conclude that at least one of these variables X₄, X₅, and X₆ is important for explaining variation in Y.

Answer 1

sample size n=			30
SSE for complete model :SSEc =(1-R^2)*TSS=			320
SSE for reduced model :SSER ==(1-R^2)*TSS=			423.85
c =coefficients in complete model =			5
r =coefficient in reduced model =			2
Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) =					2.60
numerator df =(c-r) =			3
and denominator df =(n-c-1) =			24
p value =			0.0758

since p value >0.05:

C.

The test statistic is 2.60, and we conclude that none of these explanatory variables are statistically associated with variation in Y.